Born in Missouri, Gillespie grew up in Oklahoma where he graduated from Shawnee High School in 1956.
(magna cum laude and Phi Beta Kappa) with a major in physics from Rice University.
Gillespie received his Ph.D. from Johns Hopkins University in 1968 with a dissertation in experimental elementary particle physics under Aihud Pevsner.
Part of his dissertation derived procedures for stochastically simulating high-energy elementary particle reactions using digital computers, and Monte Carlo methodology would play a major role in his later work.
From 1968 to 1971, Gillespie was a Faculty Research Associate at the University of Maryland College Park's Institute for Molecular Physics.